Your lx shifters will be fine, I have used stx basic shifter most of my life, including my late teens riding many miles a week pre car ownership, and broke my first one in covid on a bike twenty years old. So quality wise mid nineties shifters are pretty good even at stx.
This site, and the desire to have what I couldnt afford as a teen.. have made me a bit of a snob but actually looking back , i know there was a little more weight, but my budget was stx with occasional lx parts in the nineties and i think i got a lot of mileage out of it, and still base what looks good against the old stx se groupset.
I went xt v brake with the best ones they made, and avid levers, many years ago ,tried other shifters wasn't impressed enough to spend money.
During covid I refreshed one of my Kona's and fitted all 8sp xt mint used, in fairness I think that's about the pinnacle for shimano, the derailleurs are crazy good quality and the shifting is a little more precise, it all looks nice with a little polished and chrome surface so looks wise easy winner too for me.. but I have a bike that came xtr, early 9sp and I really don't think its any better, lighter perhaps, but not enough to be worth the premium in use.
I am not a huge fan of the grey xtr finish either, especially on cranks that looked scruffy in no time.. madness.
Because of the lower price point and number of bikes versus time, all my plotting for more bikes is down with stx and lx now, built with good condition parts I will never wear it out with 7 / 8 bikes to play with..!
I do spy some very boutique parts in your build, and arguably for looks the polished look lx shifters would look perfect but if you want 9spd I think the budget xtr grey is a great shout. From memory the rear derailleur has a polished cage and same grey body, and you can buy anything from that groupset for sensible money nos if you are patient , I found some bits to replace bashed up bits on a mates bike easily enough last year.
